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It is well known that the microstructures of the transition-metal oxides(refs 1-3), including the high-transition-temperature (high-Tc) copper oxidesuperconductors (refs 4-7), are complex. This is particularly so when there areoxygen interstitials or vacancies (ref.8), which influence the bulk properties.For example, the oxygen interstitials in the spacer layers separating thesuperconducting CuO2 planes undergo ordering phenomena in Sr(2)O(1+y)CuO(2)(ref. 9), YBa(2)Cu(3)O(6+y) (ref. 10) and La(2)CuO(4+y) (refs 11-15) thatinduce enhancements in the transition temperatures with no changes in holeconcentrations. It is also known that complex systems often have ascale-invariant structural organization16, but hitherto none had been found inhigh-Tc materials. Here we report that the ordering of oxygen interstitials inthe La(2)O(2+y) spacer layers of La(2)CuO(4+y) high-Tc superconductors ischaracterized by a fractal distribution up to a maximum limiting size of 400microns. Intriguingly, these fractal distributions of dopants seem to enhancesuperconductivity at high temperature.

Scale-free structural organization of oxygen interstitials in La2CuO4+y